Question

A line goes through the points (-6, -8) and (12, 7).

Answer 1

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have (-6, -8), (12, 7).

Substitute:

$m=\dfrac{7-(-8)}{12-(-6)}=\dfrac{7+8}{12+6}=\dfrac{15}{18}=\dfrac{5}{6}$

The slope-point form:

$y-y_1=m(x-x_1)$

We have m = 5/6 and (12, 7).

Substitute:

$y-7=\dfrac{5}{6}(x-12)$

The slope-intercept form:

$y=mx+b$

$y-7=\dfrac{5}{6}(x-12)\\\\y-7=\dfrac{5}{6}x-\dfrac{5}{6}\cdot12}\\\\y-7=\dfrac{5}{6}x-\dfrac{5}{1}\cdot2\\\\y-7=\dfrac{5}{6}x-10\qquad|+7\\\\y=\dfrac{5}{6}x-3$